(a) Two independent r v s, X 1 and X 2 , take on values 1,2 with equal probabilities Without calculations, guesswhether all possible values of the sum X 1 X 2 are also equally likely Give a heuristic explanation Using the convolution formula, find all probabilities fn P(X 1 X 2 n) Graph fn as a fun...

For X 1r the sum SXX2 takes on values 2 2r One should not expect these values to be equall ...

(a) Two independent r.v.s, X 1 and X 2 , take on values 1,2 with equal probabilities....

Question:

(a) Two independent r.v.’s, X₁ and X₂, take on values 1,2 with equal probabilities. Without calculations, guesswhether all possible values of the sum X₁+ X₂ are also equally likely. Give a heuristic explanation. Using the convolution formula, find all probabilities fn = P(X₁ +
X₂ = n). Graph fn as a function of n. (You may consider only integer n, or connect neighbor points by straight lines.)

(b) Do the same for X₁ and X₂ taking on equiprobable values 1, ..., r for a natural r.

Fantastic news! We've Found the answer you've been seeking!